We characterize the existence of Pareto optimal elements for a family of not necessarily total preorders on a compact topological space. We identify a rather general semicontinuity assumption, called weak upper semicontinuity, under which there exist Pareto optimal elements. We also show that weak upper semicontinuity of each individual preorder is a necessary and sufficient condition for determining the Pareto optimal elements by solving the classical multi-objective optimization problem in case that each function is upper semicontinuous and order-preserving for the respective preorder, and each preorder satisfies a condition of weak separability.

Pareto optimality on compact spaces in a preference-based setting under incompleteness

Paolo Bevilacqua;Gianni Bosi;Massimiliano Kaucic;
2019-01-01

Abstract

We characterize the existence of Pareto optimal elements for a family of not necessarily total preorders on a compact topological space. We identify a rather general semicontinuity assumption, called weak upper semicontinuity, under which there exist Pareto optimal elements. We also show that weak upper semicontinuity of each individual preorder is a necessary and sufficient condition for determining the Pareto optimal elements by solving the classical multi-objective optimization problem in case that each function is upper semicontinuous and order-preserving for the respective preorder, and each preorder satisfies a condition of weak separability.
Pubblicato
https://www.worldscientific.com/doi/abs/10.1142/S0218488519500119
File in questo prodotto:
File Dimensione Formato  
BosietalParetoIJUFKS.pdf

Open Access dal 09/03/2020

Tipologia: Bozza finale post-referaggio (post-print)
Licenza: Copyright Editore
Dimensione 563.35 kB
Formato Adobe PDF
563.35 kB Adobe PDF Visualizza/Apri
s0218488519500119.pdf

Accesso chiuso

Tipologia: Documento in Versione Editoriale
Licenza: Copyright Editore
Dimensione 348.42 kB
Formato Adobe PDF
348.42 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2939421
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact